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XAT 2015 Quant & DI

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Quantitative Reasoning and Data Interpretation section in XAT 2015 had 31 questions. Detailed explanation and video solution to questions have been provided.

  1. What is the sum of the following series?   -64, -66, -68, ..... , -100

    1. -1458
    2. -1558
    3. -1568
    4. -1664
    5. None of the above
  2. The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

    1. 31%
    2. 22%
    3. 15%
    4. 13%
    5. 11%
  3. Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively. Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?

    1. 0.004
    2. 0.006
    3. 0.216
    4. 0.994
    5. 0.996
  4. The figure below has been obtained by folding a rectangle. The total area of the figure (as visible) is 144 square meters. Had the rectangle not been folded, the current overlapping part would have been a square. What would have been the total area of the original unfolded rectangle?

    xat 2015 quant question 4 rectangle

    1. 128 square meters
    2. 154 square meters
    3. 162 square meters
    4. 172 square meters
    5. None of the above
  5. A solid metal cylinder of 10 cm height and 14 cm diameter is melted and re-cast into two cones in the proportion of 3 : 4 (volume), keeping the height 10 cm. What would be the percentage change in the flat surface area before and after?

    1. 9%
    2. 16%
    3. 25%
    4. 50%
    5. None of the above
  6. A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7√2 ft. and cost of construction is Rs. 100 per sq. ft. Find the lowest possible cost to construct 50% of the total road.

    1. Rs.70,400
    2. Rs.1,25,400
    3. Rs.1,40,800
    4. Rs.2,35,400
    5. None of the above
  7. Product M is produced by mixing chemical X and chemical Y in the ratio of 5 : 4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 : 3. Chemical Y is prepared by mixing raw materials, B and C, in the ratio of 2 : 1. Then the final mixture is prepared by mixing 864 units of product M with water. If the concentration of the raw material B in the final mixture is 50%, how much water had been added to product M?

    1. 328 units
    2. 368 units
    3. 392 units
    4. 616 units
    5. None of the above
  8. Find the equation of the graph shown below.

    parabola

    1. y = 3x - 4
    2. y = 2x2 - 40
    3. x = 2y2 - 40
    4. y = 2x2 + 3x - 19
    5. x = 2y2 + 3y - 19
  9. Two diagonals of a parallelogram intersect each other at coordinates (17.5, 23.5). Two adjacent points of the parallelogram are (5.5, 7.5) and (13.5, 16). Find the lengths of the diagonals.

    1. 15 and 30
    2. 15 and 40
    3. 17 and 30
    4. 17 and 40
    5. Multiple solutions are possible
  10. In the diagram below, CD = BF = 10 units and ∠CED = ∠BAF = 30o. What would be the area of triangle AED? (Note: Diagram below may not be drawn to scale.)

    XAT 2015 geometry triangles

    1. 100 x (\\sqrt{2}\\) + 3)
    2. \\frac{100}{(\sqrt3 + 4)}\\)
    3. \\frac{50}{(\sqrt3 + 4)}\\)
    4. 50 x (\\sqrt{3}\\) + 4)
    5. None of the above
  11. If f(x2 – 1) = x4 – 7x2 + k1 and f(x3 – 2) = x6 – 9x3 + k2 then the value of (k2 – k1) is _____

    1. 6
    2. 7
    3. 8
    4. 9
    5. None of the above
  12. In the beginning of the year 2004, a person invests some amount in a bank. In the beginning of 2007, the accumulated interest is Rs. 10,000 and in the beginning of 2010, the accumulated interest becomes Rs. 25,000. The interest rate is compounded annually and the annual interest rate is fixed. The principal amount is:

    1. Rs. 16,000
    2. Rs. 18,000
    3. Rs. 20,000
    4. Rs. 25,000
    5. None of the above
  13. The taxes for various income slabs are given below:

    Income Slab (I) Tax rate
    I ≤ 500 0
    500 < I ≤ 2000 5%
    2000 < I ≤ 5000 10%
    5000 < I < 10,000 15%

    There are 15 persons working in an organization. Out of them 3 to 5 persons are falling in each of the income slabs mentioned above. Which of the following is the correct tax range of the 15 person? (e.g., If one is earning Rs. 2000, the tax should be : 500 * 0 + 1500 * 0.05)

    1. 1350 to 7350, both excluded
    2. 1350 to 9800, both included
    3. 2175 to 7350, both excluded
    4. 2175 to 9800, both included
    5. None of the above
  14. If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of \\frac{(a + b) + (c + d)}{(a + b) + (c - d)}\\) would be:

    1. 47
    2. 49
    3. 51
    4. 96
    5. None of the above

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